Problem: The geometric sequence $(a_i)$ is defined by the formula: $a_1 = \dfrac{1}{9}$ $a_i = 3a_{i-1}$ What is $a_{2}$, the second term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $\dfrac{1}{9}$ and the common ratio is $3$ The second term is simply the first term times the common ratio. Therefore, the second term is equal to $a_2 = \dfrac{1}{9} \cdot 3 = \dfrac{1}{3}$.